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Measurements

Learn about the International System of Units (SI Units) and how to make meaningful observations. Explore topics such as mass, volume, density, and temperature conversions. Practice with significant figures, scientific notation, and dimensional analysis.

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Measurements

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  1. Measurements Measurements make observations meaningful

  2. International System of Units (SI Units) • Uses the metric system • Based on units of 10

  3. SI Units

  4. Mass and weight are NOT the same thing Weight is dependant upon gravity, mass is not Mass

  5. Temperature • Kelvin is the SI unit, but Celsius (C) is often used • K = C + 273 Practice: • Convert 25oC to K. • Convert 352K to oC. • Convert -15oC to K. • Heat and temperature are not the same thing • Heat is a type of energy • Temperature is a measurement of energy

  6. Important Temperatures • Freezing Points for water • 0oC = 273K = 32oF • Boiling Points for water • 100oC = 373K = 212oF • Absolute zero • 0 K (-273oC) • Theoretically, all movement stops at this temperature

  7. Volume • Cubic meter (m3) is the SI unit, but liter (or milliliter) is often used • Useful Information: • Cubic centimeter (cm3 or cc) = milliliter (mL) • 1cc = 1mL

  8. Moles • Used to measure the amount (quantity) of something • 1 mole = 6.02 x 1023 particles

  9. Density • How much “stuff” in a given area • Density of water (at 250C) = 1.00g/mL • D = m/v

  10. Density Practice • A rock has a mass of 3.5kg and a volume of 7.0m3. What is the rock’s density? • An object’s density is 8.0g/cm3 and its mass is 1.5g. What is the object’s volume? • What would the mass be of a 25mL sample of an object with a density of 0.047g/mL?

  11. Base Units of the Metric System * Reference Table D

  12. SI Prefixes * Reference Table C

  13. Kangaroos Hop Down Large Green Mountains During Christmas Morning As you move left, move the decimal to the left As you move right, move the decimal to the right Metric System Conversions

  14. Convert each measurement 1. 873cm m • 0.05L mL 3. 1200mg kg 4. 75dag hg 5. 560dm km

  15. Significant Figures • Indicate the precision of a number • Used for measurements

  16. Rules for determining Sig Figs • All non-zero numbers are significant • Zeros sandwiched between significant figures are always significant. • Zeros before the first non-zero number are not significant. These zeros can be thought of as “place holders” • Zeros at the end of a number are only significant when they are decimals.

  17. If the decimal is Absent in a measurement, start on the Atlantic side (right side of the number) with the first nonzero digit. All the preceding digits are significant. If the decimal is Present in a measurement, start on the Pacific side (left side of the number) with the first nonzero digit. All the following digits are significant. Atlantic – Pacific Rule Pacific Atlantic

  18. Sig Fig Practice • 803 • 60.56 • 5.780 • 0.0025 • 0.08150 • 200. • 1.50 x 1021

  19. Exact Numbers • Exact numbers, such as the number of people in a room, have an infinite number of significant figures. • Exact numbers are counting up how many of something are present, they are not measurements made with instruments. • Exact numbers are defined numbers, such as 1 foot = 12 inches. There are exactly 12 inches in one foot. • Therefore, if a number is exact, it DOES NOT affect the accuracy of a calculation nor the precision of the expression.

  20. Rounding Addition/Subtraction • Round your final answer to the same number of decimal places as the figure with the least number of decimal places Practice • 109.05 g - 62.4 g • 2.1 g 12.59 g + 34.73 g

  21. Rounding Multiplication/Division • Round your final answer to the same number of significant figures as the number with the least number of significant figures Practice 2. The mass of a solid is 3.60g and its volume is 1.8cm3. What is the density of the solid? • 3.127 x 8.01

  22. Scientific Notation • Used as a shorthand for writing very small or very large numbers • Always written in the form a x 10b • 1  a < 10 • Exponent will be positive for numbers greater than 1 • Exponent will be negative for numbers less than 1

  23. Practice • 103,000 = • 2 x 106 = • 0.6842 = • 8.56 x 10-4 =

  24. Adding/Subtracting • Must have the same exponent first! Change the smaller exponent into the larger one • Add/Subtract the non-exponent • Keep the same exponent Examples: • 2.7x103 + 3.2x102 • 7.58x1020 – 6.2x1021

  25. Multiplying/Dividing • Multiply/Divide non-exponent • Add/Subtract exponent Examples: • (7.2 x 10-2) (3.4 x 104) = • 7.5 x 106 = 2.5 x 102

  26. Percent Error Measured – Accepted x 100 Accepted Example: Methyl alcohol boils at 65oC, a student measures it to be 68oC. What is the percent error? * Also given on Reference Table T

  27. Dimensional Analysis • You can multiply anything by 1 and not change the value of the number • Multiplying by conversion factors is the same as multiplying by 1 • Just keep track of your units!!!!! Examples: • How many seconds are there in 5.00 days? • Calculate the number of minutes in 2.0 years? Express your answer in scientific notation.

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